Reverse time migration for inverse acoustic scattering by locally rough surfaces

Consider the inverse scattering of time-harmonic point sources by an infinite rough surface which is supposed to be a local perturbation of a plane. A novel version of reverse time migration is proposed to reconstruct the shape and location of the rough surface. The method is based on a modified Helmholtz-Kirchhoff identity associated with a special rough surface, leading to a modified imaging functional which always reaches a peak on the boundary of the rough surface for sound-soft case and penetrable case, and hits a nadir on the boundary of the rough surface for sound-hard case. Numerical experiments are presented to show the powerful imaging quality, especially for multi-frequency data.Comment: 29 pages,26 figure

Simultaneous recovery of a locally rough interface and the embedded obstacle with the reverse time migration

Consider the inverse acoustic scattering of time-harmonic point sources by an unbounded locally rough interface with bounded obstacles embedded in the lower half-space. A novel version of reverse time migration is proposed to reconstruct both the locally rough interface and the embedded obstacle. By a modified Helmholtz-Kirchhoff identity associated with a planar interface, we obtain a modified imaging functional which has been shown that it always peaks on the local perturbation of the interface and on the embedded obstacle. Numerical examples are presented to demonstrate the effectiveness of the method.Comment: 21 pages, 19 figure

Reliable controller design for nonlinear systems

This paper addresses the reliable H∞ control problems for affine nonlinear systems. Based on the Hamilton-Jacobi inequality approach developed in the H∞ control problems for affine nonlinear systems, a method for the design of reliable nonlinear control systems is presented. The resulting nonlinear control systems are reliable in that they provide guaranteed local asymptotic stability and H∞ performance not only when all control components are operational, but also in case of some component outages within a prespecified subset of control components.published_or_final_versio

Robust control of uncertain nonlinear systems

This paper considers robust H∞ control problems via state feedback and measurement feedback for a class of affine nonlinear systems with gain bounded uncertainties, and the solutions of the problems are derived in terms of smooth solutions of Hamilton-Jacobi inequalities. It is also shown that the results are extensions of the corresponding results for linear systems.published_or_final_versio